A291446 - OEIS

%I #10 Aug 29 2017 21:52:53

%S 30,42,66,78,102,110,138,182,186,222,230,246,266,282,290,318,366,374,

%T 402,434,438,498,506,518,530,582,590,602,606,618,638,642,710,782,786,

%U 806,854,890,906,942,962,1002,1010,1022,1034,1038,1106,1118,1146,1158,1166,1178,1298

%N Squarefree triprimes of the form p*q*r such that p + q + r + 1 is prime.

%C All terms are even. - _Muniru A Asiru_, Aug 29 2017

%H Charles R Greathouse IV, <a href="/A291446/b291446.txt">Table of n, a(n) for n = 1..10000</a>

%e 42 = 2*3*7 and 2 + 3 + 7 + 1 is prime, so 42 is a term.

%e 402 = 2*3*67 and 2 + 3 + 67 + 1 is prime, so 402 is a term.

%t With[{nnn=80}, Take[Times@@@Select[Subsets[Prime[Range[nnn]], {3}], PrimeQ[Total[#] + 1] &]//Union, nnn]]

%o (GAP)

%o A291446:=List(Filtered(Filtered(List(Filtered(List([1..10^6],Factors),i->Length(i)=3),Set),j->Length(j)=3),i->IsPrime(Sum(i)+1)),Product); # _Muniru A Asiru_, Aug 29 2017

%o (PARI) list(lim)=my(v=List()); forprime(p=5, lim\6, forprime(q=3, min(lim\(2*p),p-2), if(isprime(p+q+3), listput(v, 2*p*q)))); Set(v) \\ _Charles R Greathouse IV_, Aug 29 2017

%Y Subsequence of A075819, and hence of A007304.

%Y Cf. A291319.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Aug 24 2017